The middle of the line
Line the values up in order. The median is the one in the middle.
Line up by height
Poovizhi’s family has 5 members, of heights 170, 173, 165, 118 and 175 cm. They line up from the shortest to the tallest.
How tall is the person standing in the middle?
What this lesson covers
The idea
The median is the middle number of the sorted data, with equally many values below and above it; for an even number of values it is the average of the two middle numbers.
Line up by height
Poovizhi’s family has 5 members, of heights 170, 173, 165, 118 and 175 cm. They line up from the shortest to the tallest.
How tall is the person standing in the middle?
- 118 cm
- 165 cm
- 170 cm
- 175 cm
Peel from both ends
Tap the smallest number, then the biggest, then the smallest again, and so on. Keep going until the middle is left.
Equal numbers on each side
Sorted, Poovizhi’s family is 118, 165, 170, 173, 175. The middle number is 170: two numbers are below it and two are above. This is the median.
Yaangba’s family has 6 members, so no single number is in the middle. Two numbers are left, 164 and 165. The median is the average of the two: (164 + 165) ÷ 2 = 164.5.
The median is the middle number of the sorted data, with equally many values below and above it. For an even number of values it is the average of the two middle numbers.
- Data | Sorted | Median
- Poovizhi | 118, 165, 170, 173, 175 | 170
- Yaangba | 155, 160, 164, 165, 169, 173 | 164.5
- Newspaper | 10, 16, 16, 18, 20, 22, 26 | 18
Notes
The median is the middle number of the sorted data, with equally many values below and above it. For an even number of values it is the average of the two middle numbers.
Check yourself
Find the median of 7, 3, 9, 5, 1.
Answer: 5
Sorted: 1, 3, 5, 7, 9. Two numbers are below 5 and two are above it. The median is 5.
Find the median of 12, 8, 20, 4. There are 4 numbers, so use the two middle numbers.
Answer: 10
Sorted: 4, 8, 12, 20. The two middle numbers are 8 and 12, and (8 + 12) ÷ 2 = 10.
What is true about the median of any sorted data?
Sort 11 values. At which position (1st, 2nd, …) is the median? Type the position number.
Answer: 6
5 values below + 1 median + 5 values above = 11. So the median is the 6th value.
- Equally many values are below it and above it. — correct. Yes! That is why it is “the middle”.
- It is the number that appears most often.. That is something else. The median is the middle position, not the most common value.
- It is always the same as the mean.. Not always. For Poovizhi’s family the mean is 160.2 and the median is 170.